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Question
`lim_(x -> pi) sinx/(x - pi)` is equal to ______.
Options
1
2
– 1
– 2
Solution
`lim_(x -> pi) sinx/(x - pi)` is equal to – 1.
Explanation:
Given, `lim_(x -> pi) sinx/(x - pi)`
= `lim_(x -> pi) (sin(pi - x))/(-(pi - x))`
= – 1 .....`[because lim_(x -> 0) sinx/x = 1 "and" pi - x -> 0 ⇒ x -> pi]`
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